The equation of circle which touches `X` and `Y`-axes at the points `(1, 0)` and `(0,1)` respectively is

Options

A. `x^(2) + y^(2) - 4y + 3 =0`
B. `x^(2) + y^(2) - 2y - 2 =0`
C. `x^(2) + y^(2) - 2x - 2y + 2 =0`
D. `x^(2) + y^(2) - 2x - 2y + 1=0`

Answer

D

Explanation

Since , circle touches X- axis and Y-axis at points (1,0) and (0,1) respectively ,brgt So centre of circle f is (1,1) and radius is 1.
Hence equations of circle is
`(x-1^(2)) + (y -1)^(2) = 1^(2)`
`rArr x^(2) + y^(2) - 2x - 2y + 1=0`